1 . 已知是完全平方数,则( )
A.![]() | B.![]() |
C.![]() | D.![]() |
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2 . 已知,求
.
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3 . 已知的虚部可能为( )
A.![]() | B.![]() | C.1 | D.0 |
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4 . 已知,且
整除
,则
( )
A.所有的和为14.5 | B.所有的和为15.5 |
C.可能4组取值 | D.可能5组取值 |
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5 . 对于函数
,若实数
满足
,其中F、D为非零实数,则
称为函数
的“
笃志点”.
(1)若
,求函数
的“
笃志点”;
(2)已知函数
,且函数
有且只有3个“
笃志点”,求实数a的取值范围;
(3)定义在R上的函数
满足:存在唯一实数m,对任意的实数x,使得
恒成立或
恒成立.对于有序实数对
,讨论函数
“
笃志点”个数的奇偶性,并说明理由.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/942c2141d01bde6b48210c56a17fc75e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/79b752f0f189e5d8666daea73e145dff.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/018a66c847609b6598fd455445021ffe.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/79b752f0f189e5d8666daea73e145dff.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/eb270730495d3aa42e23c8b0d98ab3ae.png)
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/df18da1ecd1a83afc4544ee71f00c56b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d6d5bd01306129e4b00b7af1888975fb.png)
(2)已知函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/889100ab0ad010cf68ae0f63244c7b74.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/587f9f6a4bfc5bdc31b32b03353a0cc3.png)
(3)定义在R上的函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6945674f1cb97c868dde84129106e55f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/674429107bdd48aa75e85a30d36e7276.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6bc671b445f41402078b15e2ba6fdf8b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/eb270730495d3aa42e23c8b0d98ab3ae.png)
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2023-10-26更新
|
623次组卷
|
2卷引用:上海市复旦大学附属中学2024届高三上学期10月月考数学试题
6 . 已知
、
、
是直线
上的三点,且
,
,
切直线
于点
,又过
、
作
异于
的两切线,设这两切线交于点
.
(1)求点
的轨迹
方程;
(2)设
、
是
的轨迹
上的不同两点且不关于原点
对称,若
,
的斜率分别为
,
,问:是否存在实数
,使得当
时,
的面积是定值?如果存在,求出
的值;如果不存在,说明理由.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f9e8449aad35c5d840a3395ea86df6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/236f52e04ddbd7253f44b97c4756ef9c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b9e4f55c9c031c394638c238cdb05af2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/12396c03ef39584d65d9e8a4449addd6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f9e8449aad35c5d840a3395ea86df6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/12396c03ef39584d65d9e8a4449addd6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
(1)求点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
(2)设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/54a5d7d3b6b63fe5c24c3907b7a8eaa3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/aaf3369e0ea90e8d5cf4b6b3c45c0fd8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/88e9f7d1272b7344346b58b660aa260a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6defc43285a40f7ccb74c1cc04265eba.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/423b7ae39db552e60ee8b1d27312306f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/df64046e91b047037f19e4032e3b6de3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f132407bf1cc9d1f460d50f1b0547993.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/25dd698d57d1cf239eb8752aecaaa4f4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/df64046e91b047037f19e4032e3b6de3.png)
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名校
解题方法
7 . 已知关于x的函数
和
.
(1)若
,求x的取值范围;
(2)若关于x的不等式
(其中
)的解集
,求证:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9ce81be7dbac1bd6ad7b3b6be3c2d423.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f28b848513cf03ef4bd4bddfd49800f6.png)
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/df86b0da538701c08fb214608e062372.png)
(2)若关于x的不等式
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f5e74c814429bbef147280ecd517ffd8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/02e419fd930ea3b349e70d35de4380cf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0e383eff7191e3bbe549027ef71382aa.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/72b3185579edda8ea518daf2be3e0d30.png)
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名校
8 . 如图,已知在直三棱柱
中,F为
的中点,E为棱
上的动点,
,
,
,
,则下列结论正确的是( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/42d3a82b8e587ee890467835bc4e854c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f1f229274a6e17977cc047814212589.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e0a851907ada2ac2c3c4880a6736d28a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/92535536bd3c2761724fd058427f95a8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fcd0ced286a0fbc7e4862f8147264277.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7ea0df817e3e2cd95b9cd8f73386834c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a8a7b5adfcac0f46a4cd19da4ebb4a2b.png)
A.点![]() ![]() |
B.该直三棱柱![]() ![]() |
C.当三棱锥![]() ![]() ![]() |
D.若E是棱![]() ![]() ![]() |
您最近一年使用:0次
2023-10-14更新
|
1122次组卷
|
2卷引用:辽宁省名校联盟2023-2024学年高二上学期10月联合考试数学试题
9 .
,满足
,且有
,
.
(1)求
,
的解析式.
(2)令
的图象位于
上方的
的取值的集合为
,有
,使
中
,且满足
的
的取值只有一对.设
所对边分别为
,其中
,
是线段
上一动点.证明:
为定值
(3)在(2)的条件下
为
内部一点,求
最小值.
注:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9bd13c09822d74f612305c31ad744e73.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7cfc436062d7dd474cb4f9c512d0a3dc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4e603ec0775001fae01dc90c7e688d7a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0c1044d6a79641b2190d82a5589ce.png)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/be1ce3f01e2b6364f9a9fdaf197d5e29.png)
(2)令
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d2b9643da0c0fea4f099f9a9133d6076.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cf231f8f86fb922df4ca0c87f044cec3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7ffa80473beb3aa3da5c377df90bfe29.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9efc05267f74418011231dd344514474.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0f8917a804e6389067077a0bebecd03.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/629b10e9b8c82b97a738e06277e603a3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/24e0c10fb103930eabd5fa18e8f9bb06.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/76f0649064a085fb74c997fb507a9b6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6de1d395e6c48c0676a1488a299479d9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0dc5c9827dfd0be5a9c85962d6ccbfb1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a99f18b1eb117fed2b2970a3a86c083a.png)
(3)在(2)的条件下
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/88a00c58dd635d2a57058028777ae0bf.png)
注:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f737abc86a8a9f090ecc5c6f7d4424c2.png)
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解题方法
10 . 已知函数
和
,定义集合![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a93a16382ef1c6e4b6eeea2909f358a7.png)
(1)设
,
,若
,求m的取值范围.
(2)设
,
,
,若
,求m的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bde66f0ef8ea3ac6d6ac91a93ba69ae5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/544f91d4fb22c571db9f8481b72a0419.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a93a16382ef1c6e4b6eeea2909f358a7.png)
(1)设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a7e204b1d7ee9fec55811da546bd2d9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f220ef5339248b2971cecebb6a92294b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/44bac659eca0067a8f5217d0ce62c2c0.png)
(2)设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6436413dff637d3ae243f82bd22c4f1a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/24bbf9858659de45bd26111af7babef2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5c6d4b11a69708e588e4bbac9f2b3f6a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ecbf3b0349dc38eb54864384c6ef043e.png)
您最近一年使用:0次